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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 67268, 14 pages
http://dx.doi.org/10.1155/JAMSA/2006/67268

Large-scale stochastic hereditary systems under Markovian structural perturbations. Part II. Qualitative analysis of isolated subsystems

Department of Mathematics, The University of Texas at Arlington, Arlington 76019, TX, USA

Received 14 January 2005; Revised 26 October 2005; Accepted 26 October 2005

Copyright © 2006 G. S. Ladde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this part of the work, the convergence and stability analysis of isolated subsystems of stochastic hereditary systems under random structural perturbations is investigated. The variational comparison theorems developed in Part I are used to achieve this goal. Under algebraic conditions on the rate coefficients, time-delay, and an intensity matrix associated with the Markov chain, convergence and stability results are obtained. Furthermore, it is shown that these properties are affected by hereditary and random structural perturbations effects. It is further shown that the mathematical conditions are algebraically simple and are robust to the parametric changes. This investigation provides a basis for drawing the conclusions about the overall large-scale system.